Some definitions

There are some definitions applying to rule-based systems which give a base for the theory.

Redundant rules

There are two basic possibilities of defining redundant rules:

• a rule is redundant if there exists another rule with identical (up to variables renaming) precondition and conclusion,
• a rule is redundant if it succeeds in the same situation as another rule and both the rules have the same conclusions.

Subsumption of rules

We consider here the most general case of subsumption. A rule subsumes another rule if the following conditions hold:

• the precondition part of the first rule is weaker (more general) than the precondition of the subsumed rule,
• the conclusion part of the first rule is stronger (less general) than the conclusion of the subsumed rule.

Reduction of rules

The main idea of reduction of rules is to minimize the number of rules without influencing the potential capabilities of the system for inferring new knowledge (see [7]).

Completeness of rule-based systems

A rule-based system is complete if there exists at least one rule succeeding for any possible input situation [7].